Sir Christopher John Greenwood (born 12 May 1955) is Master of Magdalene College, Cambridge, an arbitrator of international disputes, and a former British judge at the International Court of Justice. Prior to his election, he was professor of international law at the London School of Economics and a barrister who regularly appeared as counsel before the International Court of Justice, the European Court of Human Rights, the English courts, and other tribunals.

Greenwood is the son of Captain Murray Greenwood RN and Diana Greenwood. He attended Wellingborough School. In 1976, he took a first in law from Magdalene College, Cambridge; in 1977, a first in International Law; MA in 1981. In 1976, he was president of the Cambridge Union. He's married with two daughters.

He was called to the bar at the Middle Temple in 1978 and was appointed Queen's Counsel in 1999. In 2002 he was appointed Companion of the Order of St Michael and St George (CMG) in the Queen's Birthday Honours for services to international law. He was knighted in the 2009 New Year Honours. In 2018 Queen's Birthday Honours, he was appointed Knight Grand Cross of the Order of the British Empire (GBE) for services to international justice.

Greenwood is a member of the Panel of Arbitrators for the Law of the Sea Treaty, the International Centre for Settlement of Investment Disputes, and the United Kingdom National Group at the Permanent Court of Arbitration.

He became Master of Magdalene College, Cambridge, on 1 October 2020, succeeding Rowan Williams.

Greenwood is well known for the October 2002 legal opinion tendered to the British government, entitled The Legality of Using Force Against Iraq. His legal opinion, in which Greenwood was instructed in his capacity as a QC, has been used to justify that the invasion by Britain, the United States and allied powers was sanctioned by the UN Security Council. However, the opinion was concluded in the month before the adoption of United Nations Security Council Resolution 1441 and the conclusion was stated to be dependent on one of three conditions being satisfied. These conditions (he said) were (1) "if the UN Security Council adopts a fresh resolution authorising military action against Iraq and any conditions set out in that resolution are met" – this did not happen; or (2) "under existing Security Council resolutions on the basis that the Security Council considered that (a) Iraq is in material breach of those resolutions" and (b) "that breach constitutes a threat to international peace and security in the Gulf area. This would not require a fresh Security Council authorisation of military action".

The question of whether these conditions were satisfied is controversial and unclear, since there was no further resolution which might have rendered the point clear. Alternatively, (3) "under the right of self-defence if an armed attack by Iraq against the United Kingdom or one of its allies was reasonably believed to be imminent. This would not require any action by the Security Council."

Greenwood acted as counsel for the government of the United Kingdom in relation to a number of cases in both domestic and international courts: the Ojdanic case in the International Criminal Tribunal for the Former Yugoslavia; Federal Republic of Yugoslavia v. United Kingdom in the International Court of Justice; the General Assembly request to the ICJ for an advisory opinion on the Palestinian wall (UK observations on admissibility); R (on the application of the European Roma Rights Centre and others) v. Immigration Officer at Prague Airport and others; and R (on the application of Abbasi and Mubanga) v. the Secretary of State for Foreign and Commonwealth Affairs and others.